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Factorize each of the following algebrai...

Factorize each of the following algebraic expressions:
(1) `x^2+12 x-45`
(2) `40+3x-x^2`
(3) `a^2+3a-88`
(4) `a^2-14 a-51`

Text Solution

Verified by Experts

(1) `x^2+12 x-45`
By using mid-term splitting, we get:
`=x^2+15x-3x-45`
`=x(x+15)-3(x+15)`
`=(x+15)(x-3)`

(2) `40+3x-x^2`
`=-x^2+3x+40`
By using mid-term splitting, we get:
`=-x^2+8x-5x+40`
`=-x(x-8)-5(x-8)`
`=(x-8)(-x-5)`

(3) `a^2+3a-88`
By using mid-term splitting, we get:
`=a^2+11a-8a-88`
`=a(a+11)-8(a+11)`
`=(a+11)(a-8)`

(4) `a^2-14 a-51`
By using mid-term, we get:
`=a^2+3a-17a-51`
`=a(a+3)-17(a+3)`
`=(a+3)(a-17)`
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